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Classification of invariant Einstein metrics on certain compact homogeneous spaces

  • Zaili Yan
  • Huibin Chen
  • Shaoqiang DengEmail author
Articles
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Abstract

In this paper, we study invariant Einstein metrics on certain compact homogeneous spaces with three isotropy summands. We show that, if G/K is a compact isotropy irreducible space with G and K simple, then except for some very special cases, the coset space G × G=Δ(K) carries at least two invariant Einstein metrics. Furthermore, in the case that G1;G2 and K are simple Lie groups, with KG1;KG2, and G1G2, such that G1/K and G2/K are compact isotropy irreducible spaces, we give a complete classification of invariant Einstein metrics on the coset space G1 × G2=Δ(K).

Keywords

compact Lie group Einstein metric isotropy irreducible space 

MSC(2010)

53C25 53C35 53C30 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11401425, 11626134, 11701300, 11671212 and 51535008) and K. C. Wong Magna Fund in Ningbo University.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNingbo UniversityNingboChina
  2. 2.School of Mathematical Sciences and LPMCNankai UniversityTianjinChina

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